4 problems

Let $G$ be a 6-connected simple graph. A graph is 1-apex if deleting one vertex makes it planar, and $K_6$ denotes the complete graph on six vertices. Jørgensen's conjecture. Every…

Let $G=(V,E)$ be a graph. A framework is globally $\mathcal{R}_3$-rigid if every framework in $\mathbb{R}^3$ with the same edge lengths differs from it by a composition of isometri…

Forbidden-minor family conjecture. All graphs in the $K_{k+5}$ family belong to $\operatorname{Forb}(\mathcal{P}l^{(k)})$.

A graph is $n$-apex if deleting $n$ or fewer vertices results in a planar graph. A graph is a minor of another graph if it can be obtained by contracting edges in a subgraph. Let…